Course detail

Basics of Category Theory

FSI-9TKDAcad. year: 2016/2017Winter semesterNot applicable.. year of study1  credit

The aim of the subject is to make students acquainted with fundamentals of the category theory with respect to applications, especially in computer science. Some important concrete applications will be discussed in greater detail.

Learning outcomes of the course unit

Not applicable.

Prerequisites

Not applicable.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

M. Barr, Ch. Wells: Category Theory for Computing Science, Prentice Hall, New York, 1990
J. Adámek, Matematické struktury a kategorie, SNTL, Praha, 1982
B.C. Pierce, Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991
B.C. Pierce: Basic Category Theory for Computer Scientists, The MIT Press, Cambridge, 1991
R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991
R.F.C. Walters, Categories and Computer Science, Cambridge Univ. Press, 1991

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Language of instruction

Czech, English

Work placements

Not applicable.

Aims

Not applicable.

Type of course unit

 

Lecture

20 hours, optionally

Teacher / Lecturer

Syllabus

1. Graphs and categories
2. Algebraic structures as categories
3. Constructions on categories
4. Properties of objects and morphisms
5. Products and sums of objects
6. Natural numbers objects and deduction systems
7. Functors and diagrams
8. Functor categories, grammars and automata
9. Natural transformations
10.Limits and colimits
11.Adjoint functors
12.Cartesian closed categories and typed lambda-calculus
13.The cartesian closed category of Scott domains